%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ104^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:28:29 AM UTC 2026
% Result : Theorem 1.50s 1.39s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 308 ( 79 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 344 ( 10 ~; 27 |; 18 &; 232 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 5 con; 0-2 aty)
% ( 20 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 51 ( 30 ^; 19 !; 2 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
cCKB6_NUM: $i > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK2: $i > $o ).
thf(func_def_16,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_17,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f63,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
$true = $false,
inference(forward_demodulation,[status(thm)],[f61,f42]) ).
thf(f42,plain,
( ( sK2 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( sK2 @ sK0 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f26,f38]) ).
thf(f38,plain,
( ( sK2 @ ( s @ sK0 ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( sK2 @ ( s @ sK0 ) )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f20,f26]) ).
thf(f20,plain,
( $false
= ( sK2 @ ( s @ ( s @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ Y0 ) ) ) )
& ( sK2 @ c1 ) )
=> ( sK2 @ ( s @ ( s @ sK0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ ( s @ ( s @ sK0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ ( s @ ( s @ sK0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) )
@ ( s @ ( s @ sK0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f13,f14]) ).
thf(f14,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cCKB6_NUM
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( cCKB6_NUM
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ( X1 @ c1 )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cCKB6_NUM
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ( X1 @ c1 )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.b0smmtb3oN/DTF2THF_27807.p',cCKB6_NUM_def) ).
thf(f13,plain,
( $true
!= ( cCKB6_NUM @ ( s @ ( s @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
!= ( cCKB6_NUM @ ( s @ ( s @ sK0 ) ) ) )
& ( $true
= ( cCKB6_NUM @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) )
!= $true )
& ( ( cCKB6_NUM @ X0 )
= $true ) )
=> ( ( $true
!= ( cCKB6_NUM @ ( s @ ( s @ sK0 ) ) ) )
& ( $true
= ( cCKB6_NUM @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i] :
( ( ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) )
!= $true )
& ( ( cCKB6_NUM @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i] :
( ( ( cCKB6_NUM @ X0 )
= $true )
=> ( ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i] :
( ( cCKB6_NUM @ X0 )
=> ( cCKB6_NUM @ ( s @ ( s @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.b0smmtb3oN/DTF2THF_27807.p',cCKB6_L4000) ).
thf(f26,plain,
! [X1: $i] :
( ( $true
= ( sK2 @ ( s @ X1 ) ) )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( ( sK2 @ X1 )
=> ( sK2 @ ( s @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( sK2 @ ( s @ Y0 ) ) ) )
& ( sK2 @ c1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f61,plain,
( $true
= ( sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK0 ) ) ),
inference(forward_demodulation,[status(thm)],[f59,f22]) ).
thf(f22,plain,
( $true
= ( sK2 @ c1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f59,plain,
( ( $false
= ( sK2 @ c1 ) )
| ( $true
= ( sK2 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true
= ( sK2 @ sK0 ) )
| ( $true = $false )
| ( $false
= ( sK2 @ c1 ) ) ),
inference(superposition,[status(thm)],[f51,f35]) ).
thf(f35,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK3 @ X1 ) ) )
| ( ( X1 @ c1 )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i > $o] :
( ( ( X1 @ c1 )
= $false )
| ( $true
= ( X1 @ sK0 ) )
| ( ( ( X1 @ ( sK3 @ X1 ) )
=> ( X1 @ ( s @ ( sK3 @ X1 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) )
@ ( sK3 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ c1 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) )
= $false )
| ( ( X1 @ c1 )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) )
& ( X1 @ c1 ) )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ Y0 ) ) ) )
& ( X1 @ c1 ) )
=> ( X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ Y1 ) ) ) )
& ( Y0 @ c1 ) )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ Y2 ) ) ) )
& ( Y1 @ c1 ) )
=> ( Y1 @ Y0 ) ) )
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f12,f14]) ).
thf(f12,plain,
( $true
= ( cCKB6_NUM @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f51,plain,
( $false
= ( sK2 @ ( sK3 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[status(thm)],[f49,f22]) ).
thf(f49,plain,
( ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ( $false
= ( sK2 @ c1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ( $true = $false )
| ( $false
= ( sK2 @ c1 ) ) ),
inference(forward_demodulation,[status(thm)],[f47,f42]) ).
thf(f47,plain,
( ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ( $true
= ( sK2 @ sK0 ) )
| ( $false
= ( sK2 @ c1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $false
= ( sK2 @ ( sK3 @ sK2 ) ) )
| ( $true = $false )
| ( $false
= ( sK2 @ c1 ) )
| ( $true
= ( sK2 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f26,f34]) ).
thf(f34,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( s @ ( sK3 @ X1 ) ) )
= $false )
| ( ( X1 @ c1 )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ104^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 11:32:57 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.44 ---- Original DTF file ---
% 0.20/0.44 thf(spec,logic,$$dhol).
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % File : PUZ104^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.20/0.44 % Domain : Puzzles
% 0.20/0.44 % Problem : TPS problem from CHECKERBOARD-THMS
% 0.20/0.44 % Version : Especial.
% 0.20/0.44 % English :
% 0.20/0.44
% 0.20/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.44 % Source : [Bro09]
% 0.20/0.44 % Names : tps_0631 [Bro09]
% 0.20/0.44
% 0.20/0.44 % Status : Theorem
% 0.20/0.44 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.20/0.44 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.20/0.44 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.20/0.44 % Maximal formula atoms : 2 ( 2 avg)
% 0.20/0.44 % Number of connectives : 13 ( 0 ~; 0 |; 1 &; 9 @)
% 0.20/0.44 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.44 % Maximal formula depth : 6 ( 4 avg)
% 0.20/0.44 % Number of types : 2 ( 0 usr)
% 0.20/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.44 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.20/0.44 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.20/0.44 % SPC : TH0_THM_EQU_NAR
% 0.20/0.44
% 0.20/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.44 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 thf(c1_type,type,
% 0.20/0.44 c1: $i ).
% 0.20/0.44
% 0.20/0.44 thf(s_type,type,
% 0.20/0.44 s: $i > $i ).
% 0.20/0.44
% 0.20/0.44 thf(cCKB6_NUM_type,type,
% 0.20/0.44 cCKB6_NUM: $i > $o ).
% 0.20/0.44
% 0.20/0.44 thf(cCKB6_NUM_def,definition,
% 0.20/0.44 ( cCKB6_NUM
% 0.20/0.44 = ( ^ [Xx: $i] :
% 0.20/0.44 ! [Xp: $i > $o] :
% 0.20/0.44 ( ( ( Xp @ c1 )
% 0.20/0.44 & ! [Xw: $i] :
% 0.20/0.44 ( ( Xp @ Xw )
% 0.20/0.44 => ( Xp @ ( s @ Xw ) ) ) )
% 0.20/0.44 => ( Xp @ Xx ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(cCKB6_L4000,conjecture,
% 0.20/0.44 ! [Xx: $i] :
% 0.20/0.44 ( ( cCKB6_NUM @ Xx )
% 0.20/0.44 => ( cCKB6_NUM @ ( s @ ( s @ Xx ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 ------------------------
% 1.50/1.35 ---- Embedded in THF ---
% 1.50/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.35 %%% Generated on Tue Feb 24 11:32:58 EST 2026
% 1.50/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.35 %%% Logic specification used:
% 1.50/1.35 %%% thf(spec, logic, $$dhol).
% 1.50/1.35
% 1.50/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.b0smmtb3oN/DTF2DTF27807.p
% See solution above
% 1.50/1.35 ------------------------
% 1.50/1.36 ---- Cleaned THF ---
% 1.50/1.36 thf(c1_type,type,
% 1.50/1.36 c1: $i ).
% 1.50/1.36
% 1.50/1.36 thf(s_type,type,
% 1.50/1.36 s: $i > $i ).
% 1.50/1.36
% 1.50/1.36 thf(cCKB6_NUM_type,type,
% 1.50/1.36 cCKB6_NUM: $i > $o ).
% 1.50/1.36
% 1.50/1.36 thf(cCKB6_NUM_def,definition,
% 1.50/1.36 ( cCKB6_NUM
% 1.50/1.36 = ( ^ [Xx: $i] :
% 1.50/1.36 ! [Xp: $i > $o] :
% 1.50/1.36 ( ( ( Xp @ c1 )
% 1.50/1.36 & ! [Xw: $i] :
% 1.50/1.36 ( ( Xp @ Xw )
% 1.50/1.36 => ( Xp @ ( s @ Xw ) ) ) )
% 1.50/1.36 => ( Xp @ Xx ) ) ) ) ).
% 1.50/1.36
% 1.50/1.36 thf(cCKB6_L4000,conjecture,
% 1.50/1.36 ! [Xx: $i] :
% 1.50/1.36 ( ( cCKB6_NUM @ Xx )
% 1.50/1.36 => ( cCKB6_NUM @ ( s @ ( s @ Xx ) ) ) ) ).
% 1.50/1.36 ------------------------
% 1.50/1.38 % (27906)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_27807 for (2999ds/27Mi)
% 1.50/1.38 % (27908)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_27807 for (2999ds/2Mi)
% 1.50/1.38 % (27909)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_27807 for (2999ds/275Mi)
% 1.50/1.38 % (27905)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_27807 for (2999ds/4Mi)
% 1.50/1.38 % (27907)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27807 for (2999ds/2Mi)
% 1.50/1.38 % (27910)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27807 for (2999ds/18Mi)
% 1.50/1.38 % (27904)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27807 for (2999ds/183Mi)
% 1.50/1.38 % (27907)Instruction limit reached!
% 1.50/1.38 % (27907)------------------------------
% 1.50/1.38 % (27907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.38 % (27907)Termination reason: Unknown
% 1.50/1.38 % (27907)Termination phase: Saturation
% 1.50/1.38 % (27908)Instruction limit reached!
% 1.50/1.38 % (27908)------------------------------
% 1.50/1.38 % (27908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.38 % (27908)Termination reason: Unknown
% 1.50/1.38 % (27908)Termination phase: Saturation
% 1.50/1.38
% 1.50/1.38 % (27908)Memory used [KB]: 5373
% 1.50/1.38 % (27908)Time elapsed: 0.003 s
% 1.50/1.38 % (27908)Instructions burned: 2 (million)
% 1.50/1.38 % (27908)------------------------------
% 1.50/1.38 % (27908)------------------------------
% 1.50/1.38
% 1.50/1.38 % (27907)Memory used [KB]: 5373
% 1.50/1.38 % (27907)Time elapsed: 0.003 s
% 1.50/1.38 % (27907)Instructions burned: 2 (million)
% 1.50/1.38 % (27907)------------------------------
% 1.50/1.38 % (27907)------------------------------
% 1.50/1.38 % (27909)Refutation not found, incomplete strategy
% 1.50/1.38 % (27909)------------------------------
% 1.50/1.38 % (27909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.38 % (27909)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.38
% 1.50/1.38
% 1.50/1.38 % (27909)Memory used [KB]: 5500
% 1.50/1.38 % (27909)Time elapsed: 0.003 s
% 1.50/1.38 % (27909)Instructions burned: 2 (million)
% 1.50/1.38 % (27909)------------------------------
% 1.50/1.38 % (27909)------------------------------
% 1.50/1.38 % (27905)Instruction limit reached!
% 1.50/1.38 % (27905)------------------------------
% 1.50/1.38 % (27905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.38 % (27905)Termination reason: Unknown
% 1.50/1.38 % (27905)Termination phase: Saturation
% 1.50/1.38
% 1.50/1.38 % (27905)Memory used [KB]: 5500
% 1.50/1.38 % (27905)Time elapsed: 0.005 s
% 1.50/1.38 % (27905)Instructions burned: 5 (million)
% 1.50/1.38 % (27905)------------------------------
% 1.50/1.38 % (27905)------------------------------
% 1.50/1.38 % (27906)First to succeed.
% 1.50/1.39 % (27906)Refutation found. Thanks to Tanya!
% 1.50/1.39 % SZS status Theorem for DTF2THF_27807
% 1.50/1.39 % SZS output start Proof for DTF2THF_27807
% 1.50/1.39 thf(func_def_1, type, s: $i > $i).
% 1.50/1.39 thf(func_def_2, type, cCKB6_NUM: $i > $o).
% 1.50/1.39 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.39 thf(func_def_15, type, sK2: $i > $o).
% 1.50/1.39 thf(func_def_16, type, sK3: ($i > $o) > $i).
% 1.50/1.39 thf(func_def_17, type, ph4: !>[X0: $tType]:(X0)).
% 1.50/1.39 thf(f63,plain,(
% 1.50/1.39 $false),
% 1.50/1.39 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.50/1.39 thf(f62,plain,(
% 1.50/1.39 ($true = $false)),
% 1.50/1.39 inference(forward_demodulation,[status(thm)],[f61,f42])).
% 1.50/1.39 thf(f42,plain,(
% 1.50/1.39 ((sK2 @ sK0) = $false)),
% 1.50/1.39 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.50/1.39 thf(f41,plain,(
% 1.50/1.39 ((sK2 @ sK0) = $false) | ($true = $false)),
% 1.50/1.39 inference(superposition,[status(thm)],[f26,f38])).
% 1.50/1.39 thf(f38,plain,(
% 1.50/1.39 ((sK2 @ (s @ sK0)) = $false)),
% 1.50/1.39 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.50/1.39 thf(f37,plain,(
% 1.50/1.39 ((sK2 @ (s @ sK0)) = $false) | ($true = $false)),
% 1.50/1.39 inference(superposition,[status(thm)],[f20,f26])).
% 1.50/1.39 thf(f20,plain,(
% 1.50/1.39 ($false = (sK2 @ (s @ (s @ sK0))))),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.50/1.39 thf(f19,plain,(
% 1.50/1.39 ((((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ Y0))))) & (sK2 @ c1)) => (sK2 @ (s @ (s @ sK0)))) = $false)),
% 1.50/1.39 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.50/1.39 thf(f18,plain,(
% 1.50/1.39 (((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ (s @ (s @ sK0))))) @ sK2) = $false)),
% 1.50/1.39 inference(sigma_clausification,[status(thm)],[f17])).
% 1.50/1.39 thf(f17,plain,(
% 1.50/1.39 ($true != (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ (s @ (s @ sK0)))))))),
% 1.50/1.39 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.50/1.39 thf(f15,plain,(
% 1.50/1.39 ($true != ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ Y0))))) @ (s @ (s @ sK0))))),
% 1.50/1.39 inference(definition_unfolding,[status(thm)],[f13,f14])).
% 1.50/1.39 thf(f14,plain,(
% 1.50/1.39 (cCKB6_NUM = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ Y0))))))),
% 1.50/1.39 inference(cnf_transformation,[status(thm)],[f8])).
% 1.50/1.39 thf(f8,plain,(
% 1.50/1.39 (cCKB6_NUM = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ Y0))))))),
% 1.50/1.39 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.39 thf(f7,plain,(
% 1.50/1.39 (cCKB6_NUM = (^[X0 : $i] : (! [X1 : $i > $o] : (((X1 @ c1) & ! [X2 : $i] : ((X1 @ X2) => (X1 @ (s @ X2)))) => (X1 @ X0)))))),
% 1.50/1.39 inference(rectify,[status(thm)],[f1])).
% 1.50/1.39 thf(f1,axiom,(
% 1.50/1.39 (cCKB6_NUM = (^[X0 : $i] : (! [X1 : $i > $o] : (((X1 @ c1) & ! [X2 : $i] : ((X1 @ X2) => (X1 @ (s @ X2)))) => (X1 @ X0)))))),
% 1.50/1.39 file('/export/starexec/sandbox/tmp/tmp.b0smmtb3oN/DTF2THF_27807.p',cCKB6_NUM_def)).
% 1.50/1.39 thf(f13,plain,(
% 1.50/1.39 ($true != (cCKB6_NUM @ (s @ (s @ sK0))))),
% 1.50/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.39 thf(f11,plain,(
% 1.50/1.39 ($true != (cCKB6_NUM @ (s @ (s @ sK0)))) & ($true = (cCKB6_NUM @ sK0))),
% 1.50/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.50/1.39 thf(f10,plain,(
% 1.50/1.39 ? [X0 : $i] : (((cCKB6_NUM @ (s @ (s @ X0))) != $true) & ((cCKB6_NUM @ X0) = $true)) => (($true != (cCKB6_NUM @ (s @ (s @ sK0)))) & ($true = (cCKB6_NUM @ sK0)))),
% 1.50/1.39 introduced(definition,[],[choice_axiom])).
% 1.50/1.39 thf(f9,plain,(
% 1.50/1.39 ? [X0 : $i] : (((cCKB6_NUM @ (s @ (s @ X0))) != $true) & ((cCKB6_NUM @ X0) = $true))),
% 1.50/1.39 inference(ennf_transformation,[status(thm)],[f6])).
% 1.50/1.39 thf(f6,plain,(
% 1.50/1.39 ~! [X0 : $i] : (((cCKB6_NUM @ X0) = $true) => ((cCKB6_NUM @ (s @ (s @ X0))) = $true))),
% 1.50/1.39 inference(fool_elimination,[status(thm)],[f5])).
% 1.50/1.39 thf(f5,plain,(
% 1.50/1.39 ~! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ (s @ X0))))),
% 1.50/1.39 inference(rectify,[status(thm)],[f3])).
% 1.50/1.39 thf(f3,negated_conjecture,(
% 1.50/1.39 ~! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ (s @ X0))))),
% 1.50/1.39 inference(negated_conjecture,[status(cth)],[f2])).
% 1.50/1.39 thf(f2,conjecture,(
% 1.50/1.39 ! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ (s @ X0))))),
% 1.50/1.39 file('/export/starexec/sandbox/tmp/tmp.b0smmtb3oN/DTF2THF_27807.p',cCKB6_L4000)).
% 1.50/1.39 thf(f26,plain,(
% 1.50/1.39 ( ! [X1 : $i] : (($true = (sK2 @ (s @ X1))) | ($false = (sK2 @ X1))) )),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.50/1.39 thf(f25,plain,(
% 1.50/1.39 ( ! [X1 : $i] : (($true = ((sK2 @ X1) => (sK2 @ (s @ X1))))) )),
% 1.50/1.39 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.50/1.39 thf(f24,plain,(
% 1.50/1.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ Y0)))) @ X1))) )),
% 1.50/1.39 inference(pi_clausification,[status(thm)],[f23])).
% 1.50/1.39 thf(f23,plain,(
% 1.50/1.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ Y0))))))),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.50/1.39 thf(f21,plain,(
% 1.50/1.39 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ Y0))))) & (sK2 @ c1)))),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.50/1.39 thf(f61,plain,(
% 1.50/1.39 ($true = (sK2 @ sK0))),
% 1.50/1.39 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.50/1.39 thf(f60,plain,(
% 1.50/1.39 ($true = $false) | ($true = (sK2 @ sK0))),
% 1.50/1.39 inference(forward_demodulation,[status(thm)],[f59,f22])).
% 1.50/1.39 thf(f22,plain,(
% 1.50/1.39 ($true = (sK2 @ c1))),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.50/1.39 thf(f59,plain,(
% 1.50/1.39 ($false = (sK2 @ c1)) | ($true = (sK2 @ sK0))),
% 1.50/1.39 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.50/1.39 thf(f56,plain,(
% 1.50/1.39 ($true = (sK2 @ sK0)) | ($true = $false) | ($false = (sK2 @ c1))),
% 1.50/1.39 inference(superposition,[status(thm)],[f51,f35])).
% 1.50/1.39 thf(f35,plain,(
% 1.50/1.39 ( ! [X1 : $i > $o] : (($true = (X1 @ (sK3 @ X1))) | ((X1 @ c1) = $false) | ($true = (X1 @ sK0))) )),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.50/1.39 thf(f33,plain,(
% 1.50/1.39 ( ! [X1 : $i > $o] : (((X1 @ c1) = $false) | ($true = (X1 @ sK0)) | (((X1 @ (sK3 @ X1)) => (X1 @ (s @ (sK3 @ X1)))) = $false)) )),
% 1.50/1.39 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.50/1.39 thf(f32,plain,(
% 1.50/1.39 ( ! [X1 : $i > $o] : ((((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0)))) @ (sK3 @ X1)) = $false) | ($true = (X1 @ sK0)) | ((X1 @ c1) = $false)) )),
% 1.50/1.39 inference(sigma_clausification,[status(thm)],[f31])).
% 1.50/1.39 thf(f31,plain,(
% 1.50/1.39 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0))))) = $false) | ((X1 @ c1) = $false) | ($true = (X1 @ sK0))) )),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.50/1.39 thf(f30,plain,(
% 1.50/1.39 ( ! [X1 : $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0))))) & (X1 @ c1)) = $false) | ($true = (X1 @ sK0))) )),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.50/1.39 thf(f29,plain,(
% 1.50/1.39 ( ! [X1 : $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0))))) & (X1 @ c1)) => (X1 @ sK0)))) )),
% 1.50/1.39 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.50/1.39 thf(f28,plain,(
% 1.50/1.39 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK0))) @ X1))) )),
% 1.50/1.39 inference(pi_clausification,[status(thm)],[f27])).
% 1.50/1.39 thf(f27,plain,(
% 1.50/1.39 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1))))) & (Y0 @ c1)) => (Y0 @ sK0)))))),
% 1.50/1.39 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.50/1.39 thf(f16,plain,(
% 1.50/1.39 ($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2))))) & (Y1 @ c1)) => (Y1 @ Y0))))) @ sK0))),
% 1.50/1.39 inference(definition_unfolding,[status(thm)],[f12,f14])).
% 1.50/1.39 thf(f12,plain,(
% 1.50/1.39 ($true = (cCKB6_NUM @ sK0))),
% 1.50/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.39 thf(f51,plain,(
% 1.50/1.39 ($false = (sK2 @ (sK3 @ sK2)))),
% 1.50/1.39 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.50/1.39 thf(f50,plain,(
% 1.50/1.39 ($false = (sK2 @ (sK3 @ sK2))) | ($true = $false)),
% 1.50/1.39 inference(forward_demodulation,[status(thm)],[f49,f22])).
% 1.50/1.39 thf(f49,plain,(
% 1.50/1.39 ($false = (sK2 @ (sK3 @ sK2))) | ($false = (sK2 @ c1))),
% 1.50/1.39 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.50/1.39 thf(f48,plain,(
% 1.50/1.39 ($false = (sK2 @ (sK3 @ sK2))) | ($true = $false) | ($false = (sK2 @ c1))),
% 1.50/1.39 inference(forward_demodulation,[status(thm)],[f47,f42])).
% 1.50/1.39 thf(f47,plain,(
% 1.50/1.39 ($false = (sK2 @ (sK3 @ sK2))) | ($true = (sK2 @ sK0)) | ($false = (sK2 @ c1))),
% 1.50/1.39 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.50/1.39 thf(f45,plain,(
% 1.50/1.39 ($false = (sK2 @ (sK3 @ sK2))) | ($true = $false) | ($false = (sK2 @ c1)) | ($true = (sK2 @ sK0))),
% 1.50/1.39 inference(superposition,[status(thm)],[f26,f34])).
% 1.50/1.39 thf(f34,plain,(
% 1.50/1.39 ( ! [X1 : $i > $o] : (((X1 @ (s @ (sK3 @ X1))) = $false) | ((X1 @ c1) = $false) | ($true = (X1 @ sK0))) )),
% 1.50/1.39 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.50/1.39 % SZS output end Proof for DTF2THF_27807
% 1.50/1.39 % (27906)------------------------------
% 1.50/1.39 % (27906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.39 % (27906)Termination reason: Refutation
% 1.50/1.39
% 1.50/1.39 % (27906)Memory used [KB]: 5500
% 1.50/1.39 % (27906)Time elapsed: 0.007 s
% 1.50/1.39 % (27906)Instructions burned: 5 (million)
% 1.50/1.39 % (27906)------------------------------
% 1.50/1.39 % (27906)------------------------------
% 1.50/1.39 % (27903)Success in time 0.02 s
%------------------------------------------------------------------------------